Recent technological developments have significantly improved the sensitivity of high frequency heterodyne receivers, which now allow efficient astronomical observations at frequencies of 1 THz and above. Typical targets for these high frequency observations include the galactic center as well as extra galactic sources, where atomic and molecular transitions are largely broadened in turbulent regions. Observations at frequencies above a few THz often require a new class of back-ends, that provide a high instantaneous bandwidth of more than 5 GHz at moderate resolutions of a few hundred to a thousand frequency pixels. Also measurements in the earth's atmosphere will largely benefit from a high bandwidth device that covers the broadened lines from different altitudes. In this thesis I have developed the prototype for a new type of spectrometer, that can fulfill most of the requirements of THz astronomy and atmospheric research. The system is based on the side-band detection of phase modulated laser light: the intermediate frequency (IF) from the receiver (range up to 10 GHz) is fed to a commercial phase modulator. The modulated laser is passed through a Fabry Perot Interferometer (FPI) and then detected on a CCD. For properly matched optics, the FPI produces a ring system that contains all the spectral information of the IF input signal. The performance of the developed spectrometer depends heavily on the optical setup and parameters of its components. The overall bandwidth is defined by the phase-modulator as well as the length of the FPI, the resolution is defined by the diameter, the optical quality, and the illumination of the FPI. The sensitivity of the system is limited by the noise characteristics of the CCD and by successful carrier suppression. To characterize the performance of the spectrometer, a ray-tracing software has been developed, that simulates the electro-magnetic field distribution in the FPI, taking into account various effects like refraction, walk-off losses and optical quality of the components. The results of the simulations match well the measured spectra and can explain oscillations and other side effects observed in the spectrometer. Furthermore, one can now systematically analyze the system for a given FPI, and optimize the performance by searching the best laser beam parameters and illumination of the FPI. The results can also be used to define the requirements on the optical components for future developments.